Complex Dynamical Behavior of Locally Active Discrete Memristor-Coupled Neural Networks with Synaptic Crosstalk: Attractor Coexistence and Reentrant Feigenbaum Trees

Abstract

In continuous neural modeling, memristor coupling has been investigated widely. Yet, there is little research on discrete neural networks in the field. Discrete models with synaptic crosstalk are even less common. In this paper, two locally active discrete memristors are used to couple two discrete Aihara neurons to form a map called DMCAN. Then, the synapse is modeled using a discrete memristor and the DMCAN map with crosstalk is constructed. The DMCAN map is investigated using phase diagram, chaotic sequence, Lyapunov exponent spectrum (LEs) and bifurcation diagrams (BD). Its rich and complex dynamical behavior, which includes attractor coexistence, state transfer, Feigenbaum trees, and complexity, is systematically analyzed. In addition, the DMCAN map is implemented in hardware on a DSP platform. Numerical simulations are further validated for correctness. Numerical and experimental findings show that the synaptic connections of neurons can be modeled by discrete memristor coupling which leads to the construction of more complicated discrete neural networks.